My knowledge on quantum mechanics is limited, but I'm comforted by the fact that this will probably count for the most of you. Quantum mechanics is a rather complicated field of science that only the brightest minds in the world can fully understand. Quantum computers function on the basis of quantum mechanical phenomena.
The team at Yale built a processor out of two two qubits, artificially made atoms consisting out of billions of aluminium atoms (but acting like a single atom). These qubits can employ two energy states like regular bits (on and off), however, thanks to the magic of superposition, qubits can be placed in multiple states at the same time. For the first time, the Yale team has run simple algorithms on this chip. The qubits on the chip are connected by a quantum bus, "photons that transmit information through wires connecting the qubits".
"Our processor can perform only a few very simple quantum tasks, which have been demonstrated before with single nuclei, atoms and photons," said Robert Schoelkopf, the William A Norton Professor of Applied Physics & Physics at Yale, "But this is the first time they've been possible in an all-electronic device that looks and feels much more like a regular microprocessor."
The quantum states could only be maintained for a microsecond - enough for simple algorithms. The team will now focus their efforts on the ability to maintain the states for longer periods of time, as well as connecting more qubits to the quantum bus; with every added qubit, processing power increases exponentially.